Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-7y &= 1 \\ 6x+2y &= 6\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = -6x+6$ Divide both sides by $2$ to isolate $y$ $y = {-3x + 3}$ Substitute this expression for $y$ in the first equation. $-5x-7({-3x + 3}) = 1$ $-5x + 21x - 21 = 1$ Simplify by combining terms, then solve for $x$ $16x - 21 = 1$ $16x = 22$ $x = \dfrac{11}{8}$ Substitute $\dfrac{11}{8}$ for $x$ back into the top equation. $-5( \dfrac{11}{8})-7y = 1$ $-\dfrac{55}{8}-7y = 1$ $-7y = \dfrac{63}{8}$ $y = -\dfrac{9}{8}$ The solution is $\enspace x = \dfrac{11}{8}, \enspace y = -\dfrac{9}{8}$.